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On Fractal Distribution Function Estimation And Applications
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Book Synopsis Fractals in Probability and Analysis by : Christopher J. Bishop
Download or read book Fractals in Probability and Analysis written by Christopher J. Bishop and published by Cambridge University Press. This book was released on 2017 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Book Synopsis Mathematical and Statistical Methods for Insurance and Finance by : Cira Perna
Download or read book Mathematical and Statistical Methods for Insurance and Finance written by Cira Perna and published by Springer Science & Business Media. This book was released on 2007-12-12 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interaction between mathematicians and statisticians reveals to be an effective approach to the analysis of insurance and financial problems, in particular in an operative perspective. The Maf2006 conference, held at the University of Salerno in 2006, had precisely this purpose and the collection published here gathers some of the papers presented at the conference and successively worked out to this aim. They cover a wide variety of subjects in insurance and financial fields.
Book Synopsis Fractal Frontiers: Fractals In The Natural And Applied Sciences by : Miroslav M Novak
Download or read book Fractal Frontiers: Fractals In The Natural And Applied Sciences written by Miroslav M Novak and published by World Scientific. This book was released on 1997-03-29 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, science has developed by reducing complex situations to simple ones, analyzing the components and synthesizing the original situation. While this 'reductionist' approach has been extremely successful, there are phenomena of such complexity that one cannot simplify them without eliminating the problem itself. Recently, attention has turned to such problems in a wide variety of fields. This is in part due to the development of fractal geometry. Fractal geometry provides the mathematical tools for handling complexity. The present volume is a collection of papers that deal with the application of fractals in both traditional scientific disciplines and in applied fields. This volume shows the advance of our understanding of complex phenomena across a spectrum of disciplines. While these diverse fields work on very different problems, fractals provide a unifying formalism for approaching these problems.
Book Synopsis Fractal Algorithm and Its Application in Rock Mechanics by : Dongjie Xue
Download or read book Fractal Algorithm and Its Application in Rock Mechanics written by Dongjie Xue and published by Springer Nature. This book was released on 2022-02-22 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on learning and adapting nonlinear geometry tool in rock engineering through fractal theories, hypotheses, algorithm, practical understandings, and case studies. Understanding self-similarity and self-affinity is a prerequisite to the fractal model in rock mechanics. The book aims to provide a guide for the readers seeking to understand and build nonlinear model by fractal algorithm. The book is motivated by recent rapid advances in rock engineering in China including application of fractal theory, in addition to percolation theory. It is an essential reference to the most promising innovative rock engineering. Chapters are carefully developed to cover (1) new fractal algorithms (2) five engineering cases. This authored book addresses the issue with a holistic and systematic approach that utilizes fractal theory to nonlinear behavior in rock engineering. The book is written for researchers interested in rock and geological engineering as well as organizations engaged in underground energy practices.
Book Synopsis Markov Point Processes and Their Applications by : M. N. M. Van Lieshout
Download or read book Markov Point Processes and Their Applications written by M. N. M. Van Lieshout and published by World Scientific. This book was released on 2000 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text employs a stochastic approach to studying Markov object processes, showing that they form a flexible class of models for a range of problems involving the interpretation of spatial data. Applications can be found in many fields of study.
Book Synopsis Fractals: A Very Short Introduction by : Kenneth Falconer
Download or read book Fractals: A Very Short Introduction written by Kenneth Falconer and published by OUP Oxford. This book was released on 2013-09-26 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Book Synopsis Computational Science and Its Applications - ICCSA 2007 by : Osvaldo Gervasi
Download or read book Computational Science and Its Applications - ICCSA 2007 written by Osvaldo Gervasi and published by Springer. This book was released on 2007-08-29 with total page 1191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-volume set constitutes the refereed proceedings of the International Conference on Computational Science and its Applications. These volumes feature outstanding papers that present a wealth of original research results in the field of computational science, from foundational issues in computer science and mathematics to advanced applications in almost all sciences that use computational techniques.
Book Synopsis Fractal Solutions for Understanding Complex Systems in Earth Sciences by : V.P. Dimri
Download or read book Fractal Solutions for Understanding Complex Systems in Earth Sciences written by V.P. Dimri and published by Springer. This book was released on 2015-11-21 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with fractals in understanding problems encountered in earth science, and their solutions. It starts with an analysis of two classes of methods (homogeneous fractals random models, and homogeneous source distributions or “one point” distributions) widely diffused in the geophysical community, especially for studying potential fields and their related source distributions. Subsequently, the use of fractals in potential fields is described by scaling spectral methods for estimation of curie depth. The book also presents an update of the use of the fractal concepts in geological understanding of faults and their significance in geological modelling of hydrocarbon reservoirs. Geophysical well log data provide a unique description of the subsurface lithology; here, the Detrended Fluctuation Analysis technique is presented in case studies located off the west-coast of India. Another important topic is the fractal model of continuum percolation which quantitatively reproduce the flow path geometry by applying the Poiseuille’s equation. The pattern of fracture heterogeneity in reservoir scale of natural geological formations can be viewed as spatially distributed self-similar tree structures; here, the authors present simple analytical models based on the medium structural characteristics to explain the flow in natural fractures. The Fractal Differential Adjacent Segregation (F-DAS) is an unconventional approach for fractal dimension estimation using a box count method. The present analysis provides a better understanding of variability of the system (adsorbents – adsorbate interactions). Towards the end of book, the authors discuss multi-fractal scaling properties of seismograms in order to quantify the complexity associated with high-frequency seismic signals. Finally, the book presents a review on fractal methods applied to fire point processes and satellite time-continuous signals that are sensitive to fire occurrences.
Book Synopsis Fractal-Based Point Processes by : Steven Bradley Lowen
Download or read book Fractal-Based Point Processes written by Steven Bradley Lowen and published by John Wiley & Sons. This book was released on 2005-09-19 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated approach to fractals and point processes This publication provides a complete and integrated presentation of the fields of fractals and point processes, from definitions and measures to analysis and estimation. The authors skillfully demonstrate how fractal-based point processes, established as the intersection of these two fields, are tremendously useful for representing and describing a wide variety of diverse phenomena in the physical and biological sciences. Topics range from information-packet arrivals on a computer network to action-potential occurrences in a neural preparation. The authors begin with concrete and key examples of fractals and point processes, followed by an introduction to fractals and chaos. Point processes are defined, and a collection of characterizing measures are presented. With the concepts of fractals and point processes thoroughly explored, the authors move on to integrate the two fields of study. Mathematical formulations for several important fractal-based point-process families are provided, as well as an explanation of how various operations modify such processes. The authors also examine analysis and estimation techniques suitable for these processes. Finally, computer network traffic, an important application used to illustrate the various approaches and models set forth in earlier chapters, is discussed. Throughout the presentation, readers are exposed to a number of important applications that are examined with the aid of a set of point processes drawn from biological signals and computer network traffic. Problems are provided at the end of each chapter allowing readers to put their newfound knowledge into practice, and all solutions are provided in an appendix. An accompanying Web site features links to supplementary materials and tools to assist with data analysis and simulation. With its focus on applications and numerous solved problem sets, this is an excellent graduate-level text for courses in such diverse fields as statistics, physics, engineering, computer science, psychology, and neuroscience.
Book Synopsis Fractal Analysis by : Fernando Brambila
Download or read book Fractal Analysis written by Fernando Brambila and published by BoD – Books on Demand. This book was released on 2017-06-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis.
Book Synopsis Geomathematics: Theoretical Foundations, Applications and Future Developments by : Frits Agterberg
Download or read book Geomathematics: Theoretical Foundations, Applications and Future Developments written by Frits Agterberg and published by Springer. This book was released on 2014-07-14 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a wealth of geomathematical case history studies performed by the author during his career at the Ministry of Natural Resources Canada, Geological Survey of Canada (NRCan-GSC). Several of the techniques newly developed by the author and colleagues that are described in this book have become widely adopted, not only for further research by geomathematical colleagues, but by government organizations and industry worldwide. These include Weights-of-Evidence modelling, mineral resource estimation technology, trend surface analysis, automatic stratigraphic correlation and nonlinear geochemical exploration methods. The author has developed maximum likelihood methodology and spline-fitting techniques for the construction of the international numerical geologic timescale. He has introduced the application of new theory of fractals and multi fractals in the geostatistical evaluation of regional mineral resources and ore reserves and to study the spatial distribution of metals in rocks. The book also contains sections deemed important by the author but that have not been widely adopted because they require further research. These include the geometry of preferred orientations of contours and edge effects on maps, time series analysis of Quaternary retreating ice sheet related sedimentary data, estimation of first and last appearances of fossil taxa from frequency distributions of their observed first and last occurrences, tectonic reactivation along pre-existing schistosity planes in fold belts, use of the grouped jackknife method for bias reduction in geometrical extrapolations and new applications of the theory of permanent, volume-independent frequency distributions.
Book Synopsis Applications of Measure Theory to Statistics by : Gogi Pantsulaia
Download or read book Applications of Measure Theory to Statistics written by Gogi Pantsulaia and published by Springer. This book was released on 2016-12-22 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to put strong reasonable mathematical senses in notions of objectivity and subjectivity for consistent estimations in a Polish group by using the concept of Haar null sets in the corresponding group. This new approach – naturally dividing the class of all consistent estimates of an unknown parameter in a Polish group into disjoint classes of subjective and objective estimates – helps the reader to clarify some conjectures arising in the criticism of null hypothesis significance testing. The book also acquaints readers with the theory of infinite-dimensional Monte Carlo integration recently developed for estimation of the value of infinite-dimensional Riemann integrals over infinite-dimensional rectangles. The book is addressed both to graduate students and to researchers active in the fields of analysis, measure theory, and mathematical statistics.
Book Synopsis Biomedical Signal Analysis by : Rangaraj M. Rangayyan
Download or read book Biomedical Signal Analysis written by Rangaraj M. Rangayyan and published by John Wiley & Sons. This book was released on 2015-04-24 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book will help assist a reader in the development of techniques for analysis of biomedical signals and computer aided diagnoses with a pedagogical examination of basic and advanced topics accompanied by over 350 figures and illustrations. Wide range of filtering techniques presented to address various applications 800 mathematical expressions and equations Practical questions, problems and laboratory exercises Includes fractals and chaos theory with biomedical applications
Book Synopsis Fractals in Multimedia by : Michael F. Barnsley
Download or read book Fractals in Multimedia written by Michael F. Barnsley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications FRACTALS IN MULTIMEDIA is a result of a very successful three-day minisymposium on the same title. The event was an integral part of the IMA annual program on Mathemat ics in Multimedia, 2000-2001. We would like to thank Michael F. Barnsley (Department of Mathematics and Statistics, University of Melbourne), Di etmar Saupe (Institut fUr Informatik, UniversiUit Leipzig), and Edward R. Vrscay (Department of Applied Mathematics, University of Waterloo) for their excellent work as organizers of the meeting and for editing the proceedings. We take this opportunity to thank the National Science Foundation for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume grew out of a meeting on Fractals in Multimedia held at the IMA in January 2001. The meeting was an exciting and intense one, focused on fractal image compression, analysis, and synthesis, iterated function systems and fractals in education. The central concerns of the meeting were to establish within these areas where we are now and to develop a vision for the future.
Book Synopsis Multifractals and Chronic Diseases of the Central Nervous System by : Dipak Ghosh
Download or read book Multifractals and Chronic Diseases of the Central Nervous System written by Dipak Ghosh and published by Springer. This book was released on 2019-01-24 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily focuses on the study of various neurological disorders, including Parkinson’s (PD), Huntington (HD), Epilepsy, Alzheimer’s and Motor Neuron Diseases (MND) from a new perspective by analyzing the physiological signals associated with them using non-linear dynamics. The development of nonlinear methods has significantly helped to study complex nonlinear systems in detail by providing accurate and reliable information. The book provides a brief introduction to the central nervous system and its various disorders, their effects on health and quality of life, and their respective courses of treatment, followed by different bioelectrical signals like those detected by Electroencephalography (EEG), Electrocardiography (ECG), and Electromyography (EMG). In turn, the book discusses a range of nonlinear techniques, fractals, multifractals, and Higuchi’s Fractal Dimension (HFD), with mathematical examples and procedures. A review of studies conducted to date on neurological disorders like epilepsy, dementia, Parkinson’s, Huntington, Alzheimer’s, and Motor Neuron Diseases, which incorporate linear and nonlinear techniques, is also provided. The book subsequently presents new findings on neurological disorders of the central nervous system, namely Parkinson’s disease and Huntington’s disease, by analyzing their gait characteristics using a nonlinear fractal based technique: Multifractal Detrended Fluctuation Analysis (MFDFA). In closing, the book elaborates on several parameters that can be obtained from cross-correlation studies of ECG and blood pressure, and can be used as markers for neurological disorders.
Book Synopsis Dependence in Probability and Statistics by : Patrice Bertail
Download or read book Dependence in Probability and Statistics written by Patrice Bertail and published by Springer Science & Business Media. This book was released on 2006-09-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an account of recent developments in the field of probability and statistics for dependent data. It covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. There is a section on statistical estimation problems and specific applications. The book is written as a succession of papers by field specialists, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field.
Book Synopsis Integral, Probability, and Fractal Measures by : Gerald A. Edgar
Download or read book Integral, Probability, and Fractal Measures written by Gerald A. Edgar and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid the discussion of fractals, and follows Edgars Measure, Topology, and Fractal Geometry. With exercises throughout, this is and ideal text for beginning graduate students both in the classroom and for self-study.
